一份關(guān)于壓縮板中筋板對(duì)其屈服過程中抗扭剛度影響的一次實(shí)驗(yàn)性調(diào)查

1、KSMEInternationalJournal,VoL16,No.5,pp.599-608,2002599CharacterizationofFractureBehaviorinRepairedSkin/StiffenerStructurewithanInclinedCentralCrackKi-HyunChung",Won-HoYang,Sung-Pi!HeoDepartmentofMechanicalEngineering,SungkyunkwanUniversity,300Chunchun-Dong,Jangan-Ku,Suwon,Kyunggirdo440-746,Kore

2、aFiniteelementanalysisforthestressintensityfactortSfF)attheskin/stiffenerstructurewithinclinedcentralcrackrepairedbycompositestiffenedpanelsisdeveloped.Anumericalinvestigationwasconductedtocharacterizethefracturebehaviorandcrackgrowthbehaviorattheinclinedcrack.Inordertoinvestigatethecrackgrowthdirec

3、tion,maximumtangentialstress(MTS)criterionareused.Also,thispaperistostudytheperformanceoftheeffectivebondedcompositepatchrepairofaplatecontaininganinclinedcentralthrough-crack.Themainobjectiveofthisresearchisthevalidationoftheinclinedcrackpatchingdesign.Inthispaper,thereductionofstressintensityfacto

4、rsatthecrack-tipandpredictionofcrackgrowthdirectionaredeterminedtoevaluatetheeffectsofvariousnon-dimensionaldesignparameterincluding;compositepatchthicknessandstiffenerdistance.Wereporttheresultsoffiniteelementanalysisonthestiffenerlocationsandcrackslantanglesanddiscusstheminthispaper.Theresearchonc

5、rackedstructuresubjectedtomixedmodeloadingisaccomplishedandconcludesthatmoreworkusingadifferentapproachesisnecessary.Theauthorshopethepresentstudywillaidthosewhoareresponsiblefortherepairofdamagedaircraftstructuresandalsoprovidegeneralrepairguidelines.KeyWords:FractureMechanicsAnalysis,Skin/Stiffene

6、r,MaximumTangentialStress(MTS),CrackGrowthDirection,ReductionofStressIntensityFactor1.IntroductionDuetotherapiddevelopmentofaerospaceindustry,manyinvestigatorshavestudiedthecrackedstructuresbytherequestofsafety.Intheviewofincreasingtheservicelifeandreducingtherepaircost,theproperrepairmethodshavebee

7、nsuggested.Asasimpleandhandymethod,compositebondedpatches,whichnowarewidelyusedforcrackedstructures,canbeusedtorepairorreinforceaerospacestructuresbymodifyingtheirloaddistributionandbypassingdefectsorCorrespondingAuthor,E-mail:chungkhnature.skku.ac.krTEL:+82-31-290-7496;FAX:+82-31-290-5849Department

8、ofMechanicalEngineering,Sungkyun-kwanUniversity,300Chunchun-Dong,Jangan-Ku,Suwon,Kyunggi-do440-746,Korea.(ManuscriptRe-ceivedNovember30,2000;RevisedMarch2,2002)cracks.Inviewoftherapidlyincreasinguseofhighstrength,stiffnessandlowweight,fiber-reinforcedcompositematerialinadvancedengi-neeringstructures

9、suchashigh-performanceair-craftisdevelopedandused.Damagetolerancedesignandreliabilityofthecompositestructureshavebeenofsignificantconcernandhavealsobroughtarenewedinterestinthetheoreticalanalysis.Skin/stiffenerstructuresarecommonfeaturesofairframes(e.g.fuselages)andwingsarefrequentlymadefromstiffene

10、dsheets.Crackscanoccurinsuchstructuresinthevicinityofthestiffener.BakerandJones(1988)expressedthemanyadvantagesofemployingcompositematerialpatchesforthebondedrepairofcrackedanddamagedmetallicstructures.Bondedrepairsarelight-weight,eliminateunnecessaryfastenerholesinanalreadyweakenedanddamagedstructu

11、re,600Ki-HyunChung,Won-HoYangandSung-Pi!Heoenableloadtransfermoreevenlyandoverlargearea,thusenhancingthefatiguelifeoftherepairedstructure.Theprimaryadvantageofcompositerepairstocrackedstructuresistoimprovethedamagetoleranceoftherepairedstructure.Tothisaim,itisessentialtodemon-stratebyfractureanalysi

12、sandtestthattherepaircanretainthecrackpropagationanddamagetolerancerequirements.But,thismethodisverydifficulttoexactlyinvestigatethecrackbehavior.So,theexperimentalinvestigationandnumericalmethod(FiniteElementMethodandBoundaryElementMethodetc.)arecontinuouslyaccom-plishedtoproblemssuchashowtodistrib

13、utestressorhowtorestrainthecrack,andhowtopredictthecrackpropagationdirection.However,forasuccessfulimplementationofthisrepairtechnique,athoroughunderstandingoftheeffectofvariousdesignparametersofrepaironthecrack-tipstressintensityfactorsisneces-sary.loneandCallinan(1979,1983)studiedthecrackedpatchin

14、gusingthefiniteelementmethod.ChuandKo(1989)proposedamethodusingcollapsedisoparametricelementtopreservethesingularstresscharacteristicatthecracktip.Butthismethodrequireslargenumberofnodaldegreesoffreedom.Toovercomethisproblem,Atluri(1992)suggestedthefiniteelementalternatingmethod(FEAM)inwhichthemeshn

15、eedsnotbeveryrefinedintheregionofcracks.ChungandYang(2000)studiedthepatch'sefficiencyinviewoffracturemechanicsanddebonding.Andtheysuggestedtheoptimalpatchshapeonthereductionofstressintensityfactor.Aseriesofpreviouslyreportedresultshavesomelimitationonthehypothesisthatthestructureissubjecteduniax

16、ialloading,butmostofthestruc-turalcomponentsaresubjectedtobiaxialloading.Asthecrackdoesnotalignwithoneoftheprincipaldirections,themixedmodebehaviorwillhaveasignificanteffectonthecrackgrowthandfracturemechanics(Chue,etal.,1994).Inthispaper,theanalysisofrepairedskin/stiffenerstructurewithaninclinedcen

17、tralcrackisreported.Thefracturemechanicsanalysisatthecracktipisperformedandexpectationofthecrackpropagationdirectionistobesuggested.2.MethodofAnalysisAschematicdiagramoftheskin/stiffenerstructuretobestudiedisshowninFig.1.Analuminumrectangularskinandl-rypestiffenerpossessacentrallylocatedhorizontalth

18、rough-thicknessinclinedcrack.Topreventthepropaga-tionofcrack,anontapered0/90.boron/epoxycompositepatchisconsidered.FromthestudybyChungetal.(2000)consideringbothfracturemechanicsanddebonding,taperedpatchshapeismoreeffectivethannontaperedpatch.Skin/stiffenerandskin/patcharebondedwithepoxy.Thethickness

19、esplate,adhesivelayerandpatchare3mm,O.lmmand3mm.TheotherdimensionsandthematerialpropertiesaregiveninFig.2andTableI,respectively.Itisassumedthattheskin/stiffenersupportsanuniformtensilestress(0"0)of10MPainthey-Fig.1Configurationofskin/stiffenerplateFig.2Geometryofskin/stiffenerplatewithinclinedc

20、entralcrack(unit:mrn)CharacterizationofFractureBehaviorinRepairedSkin/StiffenerStructurewithanInclinedCentral»-601Table1Materialpropertiesofthealuminum,theboron/epoxypatch,andtheadhesivelayerYoung'smoduliShearmoduliPoisson'sratio(OPa)(OPa)E1E2E3G12G13G23)12)13V23Al-plate71.02-0.32-IPatc

21、h40.16770.16770.Q35Adhesive2.2-0.32-where(Jistheappliedload,aisthehalf-cracklength,andaistheanglebetweenthecracklineandthetensileaxis.Thestressintensityfactorcanalsobeobtainedbyconsideringthedisplacementoverthequar-ter-pointcrack-tipelementsshowninFig.3(a)2.1Stressintensityfa

22、ctorThefractureparameterforthecrackedstructureisoftengivenintermsofthestressintensityfactor.Thestressintensityfactorforacentralslantcrackoflength2ainaninfinitesheetsubjectedtoaremoteuniformuniaxialtensilestressisgivenby(Smith,1988)direction.Owingtosomeofthelimitationsofanalysis,thispaperisbasedonthe

23、followingsimplifiedassumptions.(l)Thecurvatureofthepanelisneglectedandisidealizedasaflatpanel.(2)Thebondingofthepatchandstiffenerisperfectwithoutdebonding.Thealuminumskin/stiffener,theboron/epoxycompositepatchandepoxylayermustremainlinearelastic.(3)Theadhesivelayerthicknessisrelativelythincom-paredt

24、otheplate/patchthickness,sothatageneralizedplanestressconditionisconsidered.Andtheshearstressbetweenplateandpatchistreatedasabodyforce.Theunpatchplatewithaninclinedcentralcracksituationisconsideredfirstforvalidityofthefiniteelementanalysis.Thisanalysisismadetoevaluatethestressintensityfactorsandcrac

25、kpropagationdirectionoftheplateunderserviceloadsintheabsenceofthepatchandstiffener.Theinvestigationofthepatchefficiency,bothofwithoutpatchandwithpatchareconsidered.Kr=(Jfiiisin2aKrr=(Jfiiisinacosa(1)(2)(Cooketal.,1989):KI=K1fIf-(4VB2-Vd-(4VBI-VC1)(3a)K«=KIfIf-(4uB2-ud-(4UBI-UC1)(3b)where,u=E/2(

26、1+II)istheshearmodulusofelasticity,Kisequalto(3-411)forplanestrainand(3-1I)/(1+v)forplanestress,andu.,ViareX-,y-componentsofthecrackopeningdisplacementCOD)atthecollapsedcracktipelements.IngraffaandManu(1980)proposedthecalcu-lationofstressintensityfactorforthethree-dimensionalquarter-pointcrack-tipel

27、ementsshowninFig.3(b).s,4(1V2)j211(2VB-VC+2VE-VF-2vB'+vc,-2vE'1+vp-VD')+217(-4VB+VC(4a)+4VE-vF+4v8'-vc,-4vE'+vp)+i-7l(VF+VC-2VD-vp-vc,+2vD')x,4(11I2)!211(2U8-UC+2UE-UF-2uB'+Uc,-2uE'1+up-UD')+217(-4U8+UC(4b)+4UE-UF+4uB'-Uc-4uE'+up)+7l(UF+Uc-2uD-up-uc·+

28、2uD')where,EandIIaretheYoung'smodulusandthePoisson'sratio,L1isthelengthofquarter-pointelementand17isthelocalcoordinateatthecrackfront,respectively.602Ki-HyunChung,Won-HoYangandSung-PilHeoIY.l'·11'+-1-"""9C2:=_-4ix.uCl(a)(b)Fig.3Arrangementofquarter-pointwedgee

29、lementalongsegmentofcrackfront(6a)(6b)2.2ReductionofstressintensityfactorForthemeasureofthefracturemechanicssafe-tyandpatchingefficiencycriteriaattherepairedcrack,thenondimensionalizedreductionofstressintensityfactorcanbeusedsuchthat(5)where,Ku,Kparethestressintensityfactorsfortheunpatchedandpatched

30、crackplates.Thereductionofstressintensityfactorsisveryimportanttodesignofrepairedcrackedplatebecausethisvalueimpliesthepatchefficiency.AsK*increasesthecrackpropagationde-creases,ontheotherhand,asK*decreasesthepossibilityoffractureincreases.(1963)isoneoftheearliesttheoriesdealingwithstablemixed-modec

31、rackgrowthdirectionunderstaticloading.Itpostulatesthatthecrackwillpropagationinthedirectiongovernedbythemaximumvalueofstressnormaltotheradiallinefromthecracktip.Therefore,thiscriterionassumesamodeIcrackgrowthmechanism.Mathematically,conditionforthecrackgrowthdirectioncanbeexpressedas:aa8=0.(fa8<0

32、ao'a02o;(Oe)=aeFormixed-mode,thecrackgrowthangle0basedonthiscriterionisfoundfromthefollow-ingequation:2.3PredictionofcrackgrowthdirectionInmanymixed-modecrackgrowthanalysis,thepredictionofcrackgrowthdirectionisusuallyconductedonlyattheinitialcracktip.Avarietyoftheoreticalmodelshasbeenproposedfor

33、thepredictionoffatiguecrackgrowthdirectionundermixed-modeloadings.Themaximumtangentialstresscriterion(alsocalledMTS)proposedbyErdoganandSihKr(sin+sin3:)+KI(cos+cos3:)=0(7)orKrsinO+KI(3cosO-I)=0(8)TheminimumstrainenergydensitycriterionwhichisoftencalledtheScriterionwasproposedbySih(1974),andwhichisba

34、sedonthelocaldensityoftheenergyfieldinthecracktipregion.CharacterizationofFractureBehaviorinRepairedSkin/StiffenerStructurewithanInclinedCentralc-603Formixed-modeloading,thefollowingequa-tionbasedonthiscriterionresults:Thecrackisassumedtogrowinthedirectionalongwhichthestrainenergydensityreachesminim

35、umvalue.Thestrainenergydensityfactorisdeterminedby(9)where,ai,canbeexpressedbyangle(8),Young'smodulus(E)andPoisson'sratio(II)andk;aredefinedbyk;=KJ5(i=I,II,JI)(10)asesae=O;a82>0sin28-0.92sin8+4Rk(cos28-cos8)+R/(0.92sin8-3sin8)=0where,RioistheratioKJ!K.3.FiniteElementAnalysis(11)(12)Thecon

36、ditionforcrackgrowthdirectioncanbeexpressedas:(a)(c)Thebasicgeometryofcrackedskin/stiffenerstructureconsideredinthisstudyisshownin(b)Distance(s=80mm)(d)Fig.4Finiteelementmodelingaroundcrack,inclineddegree(0)(a):0°,(b):45°,(c):90°,(d):wholemodelingofS/a=8604Ki-HyunChung,Won-HoYangandSu

37、ng-PitHeoFig.1.Considerathinelasticaluminumsheet240X360X3mmwithancentralcrackoflengthaandIrtypealuminumstiffener.Thebasicrepairconfigurationisa40X80X3mmboron/epoxycompositepatchbondedby0.3mmthickfilm-epoxyadhesive.Onceanefficientmodelisestablished,wewouldinvestigateasetofthisbasicconfigurationtostud

38、ytheeffectofstiffenerdistanceandcrackslantangle.Theslantcrackedsheetissubjectedtoaremoteuniaxialtensileloadof10MPa.Sincetheprob-lemhasnoplaneofsymmetry,itisnecessarytomodelthewholestructurebyusingthree-dimen-sional20-nodeisoparametricbrickelements.Theregionadjacenttothecrackfrontismodelledwiththesin

39、gularcrackelements.Inthesingularelementthemid-sidenodesareshiftedtothequar-ter-pointpositiontoinducetherequired(1/r)1/2stresssingularity(Fig.4).Togetbetterresults,thesingularelementsizesarekeptwithin10%ofthecracklength.FiniteelementanalysisisdoneusingacommercialABAQUScode(version5.8-8).Figure4showst

40、hefiniteelementmodelingforthestiffenerdistance80mmandthedetailconfig-urationofthecrackpartwithrespecttocrackangle.4.ResultsandDiscussionTable2Comparisonofstressintensityfactorforinclinedcrackedrectangularplates(0'0=10MPa,unit:MPav'ffiffi)InclinedSmithPresentCrackModeIiModenModeIModenAngleC&#

41、39;)SIFsiSIFsSIFsSIFs056.06!0i60.380II1054.36I9.60I58.6010.912049.5018.02I53.3420.463042.0424.27I45.3227.594032.9027.60I35.5031.41I4528.0328.03I30.2331.88I5023.1627.60i25.0231.436014.0124.2715.1327.63706.56I18.02I7.0820.52801.699.601.8210.9190000080r-r=;t7010o-"-'-'-"""&q

42、uot;"-'-=901530456075Inclinedcrackangle,8()-=_Nopateh-_hplhs-0.167._hplhs-0.333.-.-_hplhs=O.SOO_.-._-_.=:=:.i3.Smithinfinite)oL-'-'-koHInclinedcrackangle,IJ()7080r:=-r=:=)lFig.6ModenSIFwithrespecttoinclinedcrackangle(0'0=IOMPa)Fig.5ModeISIFwithrespecttoinclinedcrackangle(00=10MP

43、a)4.1RepairofinclinedcrackinunstiffenedpanelsFigures5-6showthestressintensityfactorswithrespecttotheinclinedcrackangle.Thestressintensityfactorsareobtainedintheaveragesensethroughthethickness.Toinvestigatethevalidityoftheresultsobtained,wecomparethosewithotheravailableresults.AscanbeseeninTable2andF

44、igs.5-6,theresultsareingoodagreementwithin7-10%withthoseobtainedbySmith(1988).Theseerrorsmaybecausedbythefactthatthepresentstudyconsidersthefinitemodel,butSmith'sstudyconsideredtheinfinitemodel.Figures7-8showthenondimensionalreductionofSIFwithrespecttovariousinclinedcrackangles.Fromtheresult,the

45、patchisveryefficienttorestrainthecrackgrowth.Ascom-paredwithunpatchedplate,themodeISIFsCharacterizationofFractureBehaviorinRepairedSkin/StiffenerStructurewithanInclinedCentral···605ofpatchedplatearereducedabout20-30%.ModeISIFsofthickpatcharerapidlyde-creasedastheanglebetweenloadingdir

46、ectionandinclinedcrackisdecreased.Oppositely,whenthecrackedinclinedangleisover75°,modeISIFsareincreasedasthethicknessofpatchincreases.Especially,modeISIFisnotzeroat90°ofpatchedplate.Thisphenomenonisduetothepresenceofout-of-planebendingdeformationwhichcausesthenonlinearbehaviorofmaterialand

47、geometry.ModenSIFsofpatchedplatearereducedabyabout30-45%.ThereductionofmodenSIFsisabout0.3-0.4,andwhihisindependentofinclinedangle.Ascanbeconcluded,theeffectofthickerpatchbecomesevenstronger,buttheSIFdoesnotgrowinfinitelyasthepatchthicknessincreasesbecauseoftheout-of-planebendingdeformation.And4.3Re

48、pairofinclinedcrackinstiffenedpanelsTheinfluenceofthedistanceofthestiffenertheeffectofpatchtothemodenbehaviorismoresignificantthanthemodeIbehavior.4.2PredictionofcrackgrowthdirectioninunstiffenedpanelsMostofthestudiesofcrackgrowthundermixedmodeIandnloadingshavebeenconductedusingaplatewithaninclinedc

49、entralcrackundertension.Topredictofcrackgrowthdirection,themaximumtangentialstresscriterionisexamined.Figure9showsthecrackgrowthdirectionattheunrepairedandrepairedplateswithaninclinedcentralcrack.Ascanbeseen,thepatcheffecttothecrackgrowthdirectionisrelativelyslight.Togetherwiththepatchthicknessincre

50、ase,thecrackgrowthdirectionhasatendencytogrowtowardthemodeIdirection.Asinclinedcrackangle(8lapproachesabout50-60°,whichtherangeisequalmodeISIFwithmodenSIF,thecrackgrowthdirectionoftheplaterepairedbycompositepatchbecomesperpendiculartotheapplyloadingdirection.Whentheinclinedangleapproachestheloa

51、d-ingdirection,thedifferencebetweenthepredictedcrackgrowthdirectionoftheoreticalanalysisandpredicteddirectionofpresentanalysisbecomeslanger.So,thecrackgrowthdirectionisunstable.bplhr-O.167_hplbs-O.333-+-hplbs=0.500-e-bplbs-O.667-e-hplbs=O.8334530151=-'._-O.8'<<,.;-0.69075304560Inclined

52、crackangle,8()150«:.-'-'-'-'o-+-Nopatch_hplbs=O.167_hplhs-o.333_hPlbS=O.SOO-e-bpibs-Q.667I.-=:t;J;=.-jhplbs-O.833I-3.Theoretical90.hpihr-Q.167_hplbs-O.333-+-hpihs=O.500-e-hplbs=O.667-e-hplbs-O.83330456075Inclinedcrackangle,8()15oL-'-.-'or.o.0.4.,;0.2."'=0.8"

53、;'=O.6'"'<Fig.8ReductionofmodenSIFwithrespecttoinclinedcrackangleFig.9Predictionofcrackgrowthdirectionfortherepairedplate606Ki-HyunChung,Won-HoYangandSung-Pi/HeoInclinedcrackangle,J()Fig.12ReductionofmodeISIFwithrespecttoinclinedcrackangle90_S16.Suapal<b).S18.0uupal<b)_S1a-

54、9.Suupa«:b).S1a-605pa<<:b).-0.S1.S.0pateb).-0.S1a=9.5(teb)oo8070:;30'"Cil20IS30456075Inclinedcrackangle,J()Fig.10ModeISIFwithrespecttoinclinedcrackangle(10=IOMPa)_S1a-605_S1.-S.0.51.-95<).Unstiffenede····0····<)-0-.&.&.·&

55、#183;e····<)····0HaInclinedcrackangle,J()ReductionofmodeIISIFwithrespecttoinclinedcrackangleooFig.13-.0.8.lei.:.''0.6"=e:0.4e.oS'g0.2_S1a-605uupa<<:b)-1.S1a-S.Ouupaleb)_S1a-905(uupateb).S16.Spa«:b).-0.S1S.Dpa«:b)-1·

56、3;-O··S1a_9.S(pa«:b)HaDInclinedcrackangle,8()Mode.IISIFwithrespecttoinclinedcrackangle(oo=lOMPa)o-'-'-.-'-.:.;o70_60e50l'oo!401-'"lei30f-'"Cil20Fig,111080(S=65mm,80mmand95mm)onthepredictedSIFandreductionofSIFisillustratedinFigs.10-13.Ascanbeseen,thest

57、iffenerlocationhaslessinfluenceontheSIF.But,whenthecracksizeincreases,thedistanceofstiffenerlocationmightbeplayingthemoreimportantroleinthecrackrestraintandcrackgrowthdirection.TheSIFofpatchedskin/stiffenerstructureis·decreasedabout1.5to2timesasmuchasunpatchedskin/stiffenerstructures.Wheninclinedcrackangler